Need for Speed Unbound

Firstly, ensure you are using an A+ car. I got this achievement and "Most Wanted" before finishing the prologue in my staring Supra. There are two methods of building heat:

1. Complete multiple street races within the same day/night cycle to build heat up to 5.
2. Initiate a police chase at any heat level and stay in the chase until it eventually ranks up to 5.

Now at heat 5 start a police chase either during a race or within the same police chase in step 2. I found the easiest way to escape the cops is head off-road into the countryside. If you have a helicopter above, just keep moving until it needs to refuel. Hide in the middle of a field away from roads and turn off the engine when parked. Wait long enough to escape and the achievement should pop.

Tip: I used "Kennys Test Track" (Northwest) to farm heat levels in relative safety, just going around the mud oval. Keep an eye on your health bar (bottom right) if you find it's getting low head to a gas station to repair.

In my video below I managed to go from Heat 1 to 5 and escape in one go without any repairs.

This really isn't too difficult. I found a spot on the highway with multiple entry/exit ramps and a gas station (for repairs) within a block. Keep the cop cars close and avoid taking damage as much as possible. The cop cars and SUVs will try to force you to crash into them so use caution when they approach head on. The Heat level seems to be time based. So use the traffic and some 180s to avoid the cops, exit the highway for a repair when possible and then Nitro out of there as soon as you hit Level 5. Be wary of roadblocks which will blow your tires out. And use cover (an overpass) to hide from the Choppers.